A topological approach to the existence and multiplicity of positive solutions of (p, q)-Laplacian systems

作者：Infante Gennaro^*; Maciejewski Mateusz; Precup Radu

来源：Dynamics of Partial Differential Equations, 2015, 12(3): 193-215.

DOI：10.4310/dpde.2015.v12.n3.a1

• Weak Harnack inequality
• fixed point index
• p-Laplace operator
• quasilinear elliptic system
• positive weak solution
• cone
• multiplicity
• nonexistence

In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational, quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory.

• 出版日期2015-9